The formula to calculate the modified Z score is:
\[ Z = 0.6745 \times \frac{X - M}{MAD} \]
Where:
A modified Z score is a statistical measure that indicates how many median absolute deviations (MAD) an observation is away from the median of a dataset. Unlike the traditional Z score, which uses the mean and standard deviation, the modified Z score uses the median and MAD, making it more robust to outliers. This measure is particularly useful in identifying outliers in a dataset, as it provides a more accurate representation of the data’s central tendency and variability.
Let's assume the following values:
Using the formula to calculate the modified Z score:
\[ Z = 0.6745 \times \frac{10 - 5}{2} = 1.69 \]
The modified Z score is 1.69.
